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ISSN 1088-6850(e) ISSN 0002-9947(p)

Generalized Moser lemma

Author(s): Mathieu Stiénon
Journal: Trans. Amer. Math. Soc. 362 (2010), 5107-5123.
MSC (2010): Primary 53C15, 17B62, 17B66
Posted: May 10, 2010
MathSciNet review: 2657674
Retrieve article in: PDF

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Abstract: We show how the classical Moser lemma from symplectic geometry extends to generalized complex structures (GCS) on arbitrary Courant algebroids. For this, we extend the notion of a Lie derivative to sections of the tensor bundle $(\otimes^i E)\otimes(\otimes^j E^*)$ with respect to sections of the Courant algebroid using the Dorfman bracket. We then give a cohomological interpretation of the existence of one-parameter families of GCS on and of flows of automorphims of identifying all GCS of such a family. In the particular case of symplectic manifolds, we recover the results of Moser. Finally, we give a criterion to detect the local triviality of arbitrary GCS which generalizes the Darboux-Weinstein theorem.

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